Bilevel Optimization in Machine Learning:  Recently, bilevel optimization has gained popularity in applications such as meta-learning, representation learning, and hyperparameter optimization (HPO). In meta-learning, [1]} proposes iMAML, modeling few-shot learning as a bilevel problem. The outer level learns parameters that optimally capture the overall structure of all the tasks, while the inner level optimally adapts to the few-shot samples. In representation learning, [2]} considers a bilevel problem where the outer level learns an optimal shared task representation and the inner level learns optimal task-specific parameters. In HPO, [3]} considers a bilevel problem where the outer level learns the optimal hyperparameters, while the inner level learns the optimal model for those hyperparameters. While meta-learning and representation learning are inherently multi-objective settings, they are treated in practice as a single-objective problem by summing the objectives over all tasks. Our formulation gives the flexibity to treat these inherently multi-objective problems as such, obtain stronger guarantees and ensuring that the loss of each individual task, rather than just the average loss, converges quickly.
